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Complexity theory is the theory of determining the necessary resources for the solution of algorithmic problems and, therefore, the limits of what is possible with the available resources. An understanding of these limits prevents the search for non-existing efficient algorithms. This textbook considers randomization as a key concept and emphasizes the interplay between theory and practice: New branches of complexity theory continue to arise in response to new algorithmic concepts, and its results - such as the theory of NP-completeness - have influenced the development of all areas of computer science. The topics selected have implications for concrete applications, and the significance of complexity theory for today's computer science is stressed throughout.

Table of Contents

Table of Contents

Introduction.

Algorithmic Problems and Their Complexity.

Fundamental Complexity Classes.

Reductions

Algorithmic Relations Between Problems.

The Theory of NP

Completeness.

NP

Complete and NP

Equivalent Problems.

The Complexity Analysis´of Problems.

The Complexity of Approximation Problems

Classical Results.

The Complexity of Black

Box Problems.

Further Complexity Classes and Relations between the Complexity Classes.